(5x-2)(x+5)=3

Solution for (5x-2)(x+5)=3 equation:

(5x-2)(x+5)=3

We move all terms to the left:

(5x-2)(x+5)-(3)=0

We multiply parentheses ..

(+5x^2+25x-2x-10)-3=0

We get rid of parentheses

5x^2+25x-2x-10-3=0

We add all the numbers together, and all the variables

5x^2+23x-13=0

a = 5; b = 23; c = -13;
Δ = b2-4ac
Δ = 232-4·5·(-13)
Δ = 789
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{789}}{2*5}=\frac{-23-\sqrt{789}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{789}}{2*5}=\frac{-23+\sqrt{789}}{10}
$